Let the length of one leg be x, then other leg length is (x+2).
Determine the length of leg of triangle by using the pythagoras theorem.
[tex]\begin{gathered} (10)^2=(x)^2+(x+2)^2 \\ 100=x^2+x^2+4x+4 \\ x^2+2x-48=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x+8)=0 \\ (x-6)(x+8)=0 \end{gathered}[/tex]So values of x is 6 and -8. Negative length is not possible. The value of x is 6.
Determine the length of other leg.
[tex]\begin{gathered} x+2=6+2 \\ =8 \end{gathered}[/tex]Thus length of legs of triangle are 6 ft and 8 ft.
